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We construct a cobordism group for embedded graphs in two different ways, first by using sequences of two basic operations, called "fusion" and "fission", which in terms of cobordisms correspond to the basic cobordisms obtained by attaching or removing a 1-handle, and the other one by using the concept of a 2-complex surface with boundary is the union of these knots. A discussion given to the question of extending Khovanov homology from links to embedded graphs, by using the KauffmanarXiv:0911.2608v1 fatcat:3trdyirev5anpe6drrup53ki3e